
Through a semi-implicit scheme, the viscous terms are handled implicitly using the variational quantum evolution equation solver and the non-linear inertial terms explicitly as source terms using classical computation. For quantum algorithms for non-linear problems, the reader is referred to separate works on quantum ordinary differential equation solvers [1]}, [2]}, Carleman linearization [3]} and a variational quantum nonlinear processing unit (QNPU) [4]}.
